Excited states of OH-(H2O)n clusters for n = 1–4: An ab initio study Gerald J. Hoffman, Pradeep K. Gurunathan, Joseph S. Francisco, and Lyudmila V. Slipchenko Citation: The Journal of Chemical Physics 141, 104315 (2014); doi: 10.1063/1.4894772 View online: http://dx.doi.org/10.1063/1.4894772 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A new four-dimensional ab initio potential energy surface for N2O–He and vibrational band origin shifts for the N2O–He N clusters with N = 1–40 J. Chem. Phys. 137, 104311 (2012); 10.1063/1.4749248 Photochemistry of water: The ( H 2 O ) 5 cluster J. Chem. Phys. 122, 184320 (2005); 10.1063/1.1896360 Interaction of lead atom with atmospheric hydroxyl radical. An ab initio and density functional theory study of the resulting complexes PbOH and HPbO J. Chem. Phys. 121, 7207 (2004); 10.1063/1.1784431 Ab initio studies of π-water tetramer complexes: Evolution of optimal structures, binding energies, and vibrational spectra of π-( H 2 O ) n (n=1–4) complexes J. Chem. Phys. 114, 4016 (2001); 10.1063/1.1343903 Comparative ab initio study of the structures, energetics and spectra of X − (H 2 O) n=1–4 [ X=F,Cl,Br,I ] clusters J. Chem. Phys. 113, 5259 (2000); 10.1063/1.1290016
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THE JOURNAL OF CHEMICAL PHYSICS 141, 104315 (2014)
Excited states of OH-(H2 O)n clusters for n = 1–4: An ab initio study Gerald J. Hoffman,1 Pradeep K. Gurunathan,2 Joseph S. Francisco,2 and Lyudmila V. Slipchenko2,a) 1
Department of Chemistry, Edinboro University of Pennsylvania, 230 Scotland Road, Edinboro, Pennsylvania 16444, USA 2 Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
(Received 12 June 2014; accepted 25 August 2014; published online 11 September 2014) Equation of motion coupled cluster calculations were performed on various structures of OH in clusters with one, two, three, and four water molecules to determine the energies of valence and charge transfer states. Motivation for these calculations is to understand the absorption spectrum of OH in water. Previous calculationson these species have confirmed that the longer wavelength transition observed is due to the A(2 ) ← X(2 ) valence transition, while the shorter wavelength transition is due to a charge-transfer from H2 O to OH. While these previous calculations identified the lowest energy charge-transfer state, our calculations have included sufficient states to identify additional solvent-to-solute charge transfer states. The minimum energy structures of the clusters were determined by application of the Monte Carlo technique to identify candidate cluster structures, followed by optimization at the level of second-order Møller-Plesset perturbation theory. Calculations were performed on two structures of OH-H2 O, three structures of OH-(H2 O)2 , four structures of OH-(H2 O)3 , and seven structures of OH-(H2 O)4 . Confirming previous calculations, as the number of water molecules increases, the energies of the excited valence and charge-transfer states decrease; however, the total number of charge-transfer states increases with the number of water molecules, suggesting that in the limit of OH in liquid water, the charge-transfer states form a band. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894772] I. INTRODUCTION
The hydroxyl radical, OH, plays a fundamentally important role in oxidative chemical processes in the atmosphere.1 However, in order to accurately model its behavior in the atmospheric environment, either for the purposes of measurement or to deduce reaction mechanisms, it is necessary to understand how it interacts with water.2–6 OH may interact with just one,2 or a few water molecules,3–6 or it may dissolve in a water droplet, which would produce an environment for the OH essentially identical to that of bulk water. The study of OH in bulk water has a long history. Interestingly, its absorption spectrum is still a topic of active research. Two particular features are observed in this spectrum: a shoulder that appears under certain conditions around 4.00 eV (310 nm), and a broad peak centered at 5.39 eV (230 nm).7 The shoulder is generally believed to be due to the A ← X valence transition familiar from the spectroscopy of the gas-phase radical, while the broad peak has been assigned to a charge transfer between the water and the OH. Two recent computational studies have shown that the transition next in energy above the A ← X transition is, in fact, a charge transfer (CT) transition, where the electron jumps from water to the OH radical, thus producing a hydroxide anion.8, 9 The objective of the present study is to obtain a more realistic and complete picture of the CT states in OH-water clusters, leading to a better understanding of such states in bulk a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/141(10)/104315/9/$30.00
water. Multiple structures for clusters of OH with two, three, and four water molecules were determined; some of these structures have not been reported previously. Calculations were performed on these cluster structures to obtain excited state energies, including CT states. In the previous studies,8, 9 only the lowest energy CT transition was calculated. However, when there are multiple water molecules present, there are multiple possible CT transitions. Indeed, even when OH is clustered with just a single H2 O, that H2 O may transfer an electron from one of several molecular orbitals. As the number of such states grows with the size of the cluster, one can imagine the formation of a CT band. The nature of such a band is still to be investigated, but recognizing the possible existence of this band may change the understanding of electronic and photochemical phenomena in liquid water. II. COMPUTATIONAL DETAILS
Except for the OH-H2 O dimers, structures for clusters were identified by Monte Carlo sampling of OH with the specified number of water molecules, followed by structure optimization using second order Møller-Plesset theory (MP2)10 on an unrestricted Hartree-Fock (UHF) reference wavefunction. The Monte Carlo computations were performed using the GAMESS computational chemistry software package.11 To speed up Monte Carlo simulations, the molecular clusters were described at a hybrid quantum-classical level. In particular, OH was treated using density functional theory (DFT) with the B3LYP exchangecorrelation functional12 and Dunning-Hay double-zeta
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basis sets with polarization functions.13 Water molecules were represented by fragments in the effective fragment potential (EFP) framework.14 DFT-based EFP1 water potentials were used.15 For the MP2 optimizations, the 6-311++G** basis set was used.16 This technique was used previously to identify candidate structures for O3 -(H2 O)n clusters, with n = 1–4.17 As for the OH-H2 O dimers, only two of the many structures identified in previous work were studied: the lowest energy structure with OH as proton donor in a hydrogen bond, and the lowest energy structure with H2 O as proton donor in a hydrogen bond. The total binding energy of each cluster was calculated at the level of MP2; no correction was made for basis set superposition error. Once structures were determined, excited state energies were computed by applying equation of motion coupled cluster methodology (EOM CC). Specifically, ionization potential (IP) versions of EOM-CC with single and double excitations (EOM-IP-CCSD)18–20 and with single, double, and triple excitations (EOM-IP-CC(2,3))21 were employed, again using the 6-311++G** basis set. In the IP technique, an additional electron is added to the cluster, making the hydroxyl radical the hydroxide ion, and closing its shell. The ionization potentials (IPs) for electrons from each occupied orbital (as many as desired, depending on computational capacity) are then calculated. The differences between each of these IPs and the lowest IP (which corresponds to the energy required to create the ground state of the radical from the ion) then give the energies of the excited states. EOM-IP-CC techniques provide a more balanced description of radicals, as spin-contamination, which often causes the accuracy of standard EOM-CC to deteriorate for open-shells, is avoided. For the OH-H2 O clusters, the first 10 electronic states were calculated; for the OH(H2 O)2 clusters, the first 15 electronic states were calculated; for the OH-(H2 O)3 clusters, 16 electronic states were calcu-
FIG. 1. Structures of OH-H2 O considered in this study.
lated; for the OH-(H2 O)4 clusters, 20 electronic states were calculated. However, EOM-CC(2,3) was not applied to the latter clusters. Finally, oscillator strengths for the transitions of interest were calculated at the level of EOM-IP-CCSD. The EOM-IP-CCSD technique has been previously applied to the OH-H2 O dimer, in the interest of investigating the effects of hemibonding between the moieties on CT transition energies; however, still, only the first CT state was investigated.22 All excited state calculations in this work, as well as calculation of the MP2 binding energies, were performed using the Q-Chem electronic structure package.23 Images of cluster structures were made using MacMolPlt.24 Images of molecular orbitals were constructed using WebMO.25 III. RESULTS AND DISCUSSION
The structures of OH-H2 O studied in this work are shown in Figure 1. These particular structures were chosen from the numerous previously calculated structures of this dimer because they are the most stable hydrogen-bonded structures, OH-1WA with OH as the hydrogen donor, and OH-1WB with H2 O as the hydrogen donor. Despite published structures for these two species to high levels of theory, we are using the MP2 optimized structures for the sake of consistency with our treatment of all other clusters in this study. Binding energies for all the clusters studied are collected in Table I.
TABLE I. Total and relative MP2 binding energies (in kcal mol−1 ) of the clusters studied. Relative energya OH-(H2 O)n−1 + H2 O → OH-(H2 O)n
Relative energyb OH-(H2 O)n−2 + (H2 O)2 → OH-(H2 O)n
Total energy
Previous calculation
OH-1WA OH-1WB
6.66 3.71
6.1c , 5.5d 3.2c , 3.8d
OH-2WA OH-2WB OH-2WC
16.14 15.82 11.01
14.1d 13.9d 9.7d
9.48 9.16 4.35
10.09 9.77 4.95
OH-3WA OH-3WB OH-3WC OH-3WD
28.86 28.44 22.72 20.46
25.60d ... 20.1d 18.9d
12.71 12.30 6.58 4.32
16.14 15.72 10.00 7.74
OH-4WA OH-4WB OH-4WC OH-4WD OH-4WE OH-4WF OH-4WG
39.64 37.03 35.00 34.96 34.77 34.27 33.98
34.80d ... ... ... ... 30.35d ...
10.78 8.17 6.14 6.10 5.91 5.41 5.12
17.44 14.83 12.80 12.76 12.57 12.07 11.78
Cluster
a
The lowest energy OH-(H2 O)n−1 structures are used for calculating relative energies. The lowest energy OH-(H2 O)n−2 structures are used for calculating relative energies. Binding energy of (H2 O)2 is 6.06 kcal/mol. c Reference 9; CCSD(T)/6-311(2+)G∗ including correction for BSSE. d Reference 6; DFT energies at the level of MPW1PW91/aug-cc-pVQZ//MPW1PW91/aug-cc-pVDZ. b
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FIG. 2. Structures of OH-(H2 O)2 considered in this study.
MP2 results compare well with previous calculations for these dimers, both at the level of CCSD(T)9 and DFT,6 to within a few tenths of a kcal mol−1 . Structures for OH-(H2 O)2 clusters are shown in Figure 2; all of these structures have been reported previously.4, 6 Structure OH-2WA has the dangling hydrogens on the waters pointing toward opposite sides of the ring while structure OH-2WB has them on the same side of the ring. Structure OH-2WC is significantly different from the other 2W clusters, with one H2 O molecule acting as a hydrogen bond acceptor to both OH and the other H2 O. This double hydrogen bond acceptor H2 O has both its hydrogens pointing outward, away from the ring; this molecule occupies a plane perpendicular to the plane of the ring. MP2 binding energies for these clusters, shown in Table I, agree to within 2 kcal mol−1 with previous DFT calculations6 and display the same trend for the three structures. Not surprisingly, relative binding energies of addition of a water molecule to OH-(H2 O)n−1 cluster, i.e., OH-(H2 O) + H2 O → OH-(H2 O)2 , also show dramatic decrease in the case of OH-2WC cluster, indicating the destabilization of the hydrogen bonded network in this cluster. Structures for OH-(H2 O)3 clusters are shown in Figure 3; of these four structures, only OH-3WB has not been previously reported.4, 6 Structure OH-3WB shares the fourmembered hydrogen-bonded ring of OH-3WA , but the orientations of the dangling hydrogens are no longer alternating. Structure OH-3WC is a variation of structure OH-2WA with an additional water molecule accepting a hydrogen bond from an H2 O in the ring. It should not be a surprise that re-
FIG. 3. Structures of OH-(H2 O)3 considered in this study.
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sults of calculations on this particular structure share much in common with those of structures OH-2WA and OH-2WB . In structure OH-3WD , unlike the other 3W structures considered, OH forms three hydrogen bonds with surrounding water molecules, more closely mimicking the behavior of OH in bulk water. Comparison of MP2 binding energies in Table I with previously calculated DFT6 binding energies for OH3WA , OH-3WC , and OH-3WD again shows agreement in the trend, with discrepancy on the order of 3 kcal mol−1 . Relative binding energies of OH-3WA and OH-3WB clusters, in which the third water builds two hydrogen bonds, are ∼12 kcal mol−1 that approximately corresponds to the energy of two hydrogen bonds. Relative binding energies in OH-3WC and OH-3WD clusters are only 4–6 kcal mol−1 , which can be rationalized by the fact that the third water builds only one hydrogen bond in these clusters. Another observation is that relative binding energies in square-like OH-3WA and OH3WB structures are higher than the corresponding energies in triangular-like OH-2WA and OH-2WB clusters. This is because square-like water complexes experience more optimal hydrogen bonds than rather constrained triangular water clusters. The structures for the seven OH-(H2 O)4 clusters considered in this study are found in Figure 4. Only structures OH-4WA and OH-4WF have been reported previously.4, 6 The MP2 total binding energies for these clusters are found in Table I, and compared with DFT values6 for the two previously reported structures. The structures are ordered in terms of decreasing binding energies, though they could also be categorized according to structural similarity. Structure OH4WA is the unique pentagonal structure, with the highest total and relative binding energies. Structures OH-4WC , OH4WD , and OH-4WE are based upon square OH-(H2 O)3 structures, with an additional water accepting a hydrogen bond from one of the dangling hydrogens on the water molecules making up the square. The relative binding energies in these
FIG. 4. Structures of OH-(H2 O)4 considered in this study.
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clusters are ∼6 kcal/mol that corresponds to strength of a single newly formed H-bond. The square portions of structures OH-4WC and OH-4WD are clearly based on structure OH3WB , while the square portion of OH-4WE does not resemble either OH-3WA or OH-3WB . Structures OH-4WB , OH-4WF , and OH-4WG similarly have the OH in a square structure with three water molecules, but the fourth water molecule forms two hydrogen bonds with two adjacent moieties in the square (one as hydrogen donor, one as accepter). In OH-4WB , the fourth water hydrogen bonds with two adjacent waters with relative binding energy of ∼8 kcal/mol, while the OH lies in a different part of the square. In both OH-4WF and OH4WG , OH acts as hydrogen bond acceptor to the fourth water molecule, such that the OH participates in hydrogen bonding with three water molecules. Relative binding energies of adding the fourth water in these clusters are almost 3 kcal/mol lower than in OH-4WB , in accord with observation that OH is a weaker hydrogen bond acceptor than a water. The difference between OH-4WF and OH-4WG lies in the orientations of the dangling hydrogens of the two water molecules in the square not participating in the interactions with the fourth, bridging water molecule. These two structures are important in understanding the effect of the number of hydrogen bonds to the OH on the CT states. Like OH-3WD , the OHs in these two structures form three hydrogen bonds with adjacent water molecules, as they would in bulk water. The structures investigated here are not an exhaustive list of possible cluster structures; a number of known structures for these clusters were not included in this investigation.6 However, this set of structures is sufficiently broad to investigate the electronic properties of OH in a variety of water cluster environments. The EOM-IP technique indicates for each state which of the molecular orbitals is being ionized. The nature of each state was determined by observing the shape and location of the principal contributing molecular orbital (MO) being ionized. The MOs with the greatest contribution to each ionization for representative clusters can be observed in Figures 5 through 8. Figure 5 depicts the MOs for dimers OH1WA and OH-1WB . Figure 6 shows MOs for clusters OH-
FIG. 5. Orbitals involved in the lowest transitions in (a) OH-1WA and (b) OH-1WB . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right. States resulting from the transition are denoted below each donor orbital.
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FIG. 6. Orbitals involved in the first three UV transitions in (a) OH-2WA and (b) OH-2WC . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right. (The fully occupied π orbital on OH has been excluded from this figure.) States resulting from the transition are denoted below each donor orbital.
2WA and OH-2WC ; the MOs for OH-2WB are not displayed because they are similar to those for OH-2WA . Figure 7 represents the MOs for clusters OH-3WA and OH-3WD ; the MOs for cluster OH-3WB resemble those of OH-3WA , and the MOs for cluster OH-3WC resemble those of OH-2WA . Figure 8 depicts the MOs for clusters OH-4WA and OH-4WF ; the MOs for clusters OH-4WB , OH-4WC , OH-4WD , and OH4WE resemble those of OH-3WA, while MOs for cluster OH4WG resemble those of OH-4WF . States resulting from the transition are denoted below each donor orbital. The leftmost MO in each figure is the half-filled OH π orbital of the ground state of the cluster; this MO is the acceptor orbital for the important transitions in each cluster. The orbitals to the right of this MO have IPs that increase from left to right, and are labeled according to what kind of transition connects them to the acceptor MO. In Figure 5, the first two donor orbitals are located on the OH: the orthogonal nonbonding π orbital, normally fully occupied in the ground state and nearly degenerate with the acceptor MO; and then the σ MO that bonds the oxygen to the hydrogen. (In Figures 6–8, the image of the nearly degenerate fully occupied π orbital has been excluded as it has no relevance to
FIG. 7. Orbitals involved in the first three UV transitions in (a) OH-3WA and (b) OH-3WD . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right.
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FIG. 8. Orbitals involved in the first three UV transitions in (a) OH-4WA and (b) OH-4WF . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right. (The fully occupied π orbital on OH has been excluded from this figure.) States resulting from the transition are denoted below each donor orbital.
our focus: the CT transitions.) The transition between the σ MO and the acceptor MO is the A ← X transition. Note in the figures that there is a small amount of amplitude on the oxygen accepting the hydrogen bond from the OH in the larger clusters, lending a small amount of CT character to this transition. The MOs found to the right of the OH orbitals in the figures are all located principally on the water molecules of the clusters; transitions between these and the acceptor MO give rise to full-fledged CT states. The donor MOs on water that participate in the lowest energy CT transitions consist of nonbonding oxygen 2p orbitals perpendicular to the H2 O
molecular plane; these correspond to the 1b1 orbital in the bare H2 O molecule. Note also that some of these donor MOs show significant amplitude on more than one H2 O molecule, suggesting significant electron delocalization. Transition energies calculated using EOM-IP-CCSD and EOM-IP-CC(2,3) are reported in Tables II–IV. In each table, the first row gives the energy splitting between the two components of 2 state of OH. The next row gives the energy of 2 the A( ) state of OH relative to the ground state. The section below displays the energies of the CT states for each cluster. The bottom section lists the energies of the excited electronic states originating on water molecules. Formally these states are double excitations in the EOM-IP formalism, with the double excitation consisting of ionization of one of the π orbitals on OH− , and valence excitation of an electron in one of the water molecules. It is interesting that not all the energies of the listed doubly excited states lie above those of the listed CT states, particularly in the case of CC(2,3) (Table IV). In comparing energy values between Tables II and IV, we see that the energies of all the corresponding states are within a few hundredths of an eV except for the excitations on water molecules. The application of CC(2,3) greatly lowers the energies of the water excitations. Due to their doubly excited character, these states may be significantly in error at the EOM-IP-CCSD level, but become more accurately described with inclusion of triple amplitudes in EOM-IP-CC(2,3). At the CC(2,3) level, the higher-energy CT states interleave with the water excited states. This is why there are fewer CT states listed in Table IV than in Table II.
TABLE II. EOM-IP-CCSD transition energies (eV) for OH and OH-(H2 O)n , for n = 1, 2, and 3. OH 2
A (2 ) Previous calculationa Expt.d CT
Previous calculationa Excitations on water
4.226 4.24b 4.31c 4.05 ...
OH-1WA
OH-1WB
OH-2WA
OH-2WB
OH-2WC
OH-3WA
OH-3WB
OH-3WC
OH-3WD
0.011 3.882 3.89b 3.85c
0.091 4.258
0.120 3.719 3.74b
0.125 3.738
0.027 3.949
0.177 3.529 3.65b
0.183 3.608
0.129 3.514
0.200 3.931
4.30c
7.759 10.020 14.122
5.002 7.353 11.221
6.325 6.354 8.263 8.958 12.319 12.971
6.128 6.517 8.324 8.883 12.284 12.993
5.687 7.607 8.128 10.016 11.992 14.242
6.033 6.154 7.004 8.090 8.422 9.787 12.081 12.534 13.519 6.62b
6.030 6.063 7.052 8.140 8.490 9.772 12.091 12.619 13.548
6.007 6.244 7.994 8.611 9.175 11.180 12.303 12.838
4.798 5.763 6.113 7.160 7.750 8.611 10.997 11.989 12.555
14.062 14.154 14.167 14.463 14.524 14.531
13.633 13.683 13.802 13.974 14.339 14.490
14.372 14.554 14.837
14.264 14.380 14.465 14.483
14.015 14.107 14.122 14.202 14.204
13.523 13.632 13.797 14.096
7.37b 14.123 14.173 14.315 14.864
6.89b 5.43c 13.443 13.552 13.884 14.109
14.119 14.209 14.226 14.502 14.576 14.822
a
All calculated values are EOM-CCSD using a comparable basis set. Reference 8. Reference 9. d Reference 26. b c
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TABLE III. EOM-IP-CCSD transition energies (eV) for OH and OH-(H2 O)4 . OH-4WA
OH-4WB
OH-4WC
OH-4WD
OH-4WE
OH-4WF
OH-4WG
0.176 3.467 3.50a 5.997 6.067 7.235 7.377 8.136 8.241 9.478 10.453 12.015 12.564 13.658 13.858 14.300 14.416 14.540 14.549 14.574
0.181 3.362
0.150 3.579
0.194 3.381
0.192 3.310
0.254 3.029
0.244 3.016
5.962 6.134 7.360 7.460 8.112 8.348 9.808 10.120 11.951 12.124 13.822 14.081 14.236 14.247 14.317 14.415 14.415
5.767 6.107 6.967 7.708 8.435 8.951 9.710 10.775 12.283 12.593 13.447
5.657 6.063 6.982 7.982 8.237 8.962 9.642 11.125 12.075 12.525 13.474
5.767 6.000 7.026 7.910 8.236 8.847 9.642 11.020 12.055 12.458 13.555
14.188 14.199 14.364 14.189 14.409 14.425
14.221 14.223 14.242 14.358 14.383 14.414
14.164 14.214 14.218 14.272 14.382 14.431
5.758 5.932 6.307 6.697 7.596 8.086 8.641 9.410 11.804 11.978 12.660 13.189 14.159 14.252 14.262 14.358 14.471
5.714 5.955 6.303 6.686 7.646 8.083 8.635 9.326 11.778 11.992 12.643 13.174 14.170 14.269 14.279 14.360 14.472
2
A (2 ) Previous calculation CT
Excitations on water
a
Calculated values are EOM-CCSD using a comparable basis set from Ref. 8.
TABLE IV. EOM-IP-CC(2,3) transition energies (eV) for OH and OH-(H2 O)n , for n = 1, 2, and 3. OH 2
A (2 ) Previous calculationa Expt.d CT
Previous calculationa
4.248 4.24b 4.31c 4.05 ...
OH-1WA
OH-1WB
OH-2WA
OH-2WB
OH-2WC
OH-3WA
OH-3WB
OH-3WC
OH-3WD
0.019 3.846 3.89b 3.85c
0.082 4.236
0.125 3.695 3.74b
0.130 3.713
0.028 3.911
0.172 3.501 3.65b
0.179 3.577
0.136 3.491
0.188 3.902
6.271 6.412 8.271
6.114 6.542 8.319
5.694 7.665 8.154
5.980 6.209 7.049 8.072 8.412
5.998 6.103 7.093 8.107 8.464e 8.519e
6.079 6.182 8.033 8.566
4.821 5.841 6.080 7.181 7.800
8.255 8.265 8.346 8.394 8.395 8.418 8.444 8.464e 8.519e
8.136 8.142 8.142 8.179 8.265 8.266 8.356 8.572 8.611
7.839
4.30c 5.009 7.356
7.37b
6.89b
6.62b
5.43c Excitations on water
8.133 8.153 8.170 8.185 8.616 8.640
7.725 7.773 8.123 8.147 8.448
8.247 8.292 8.350 8.396 8.455 8.467 8.523 8.691 8.735
8.168 8.214 8.337 8.362 8.377 8.470 8.477 8.592 8.680
7.953 8.006 8.013 8.254 8.347 8.446 8.476 8.488 8.519
8.342 8.347 8.354 8.390 8.419 8.469 8.541 8.596
a
All calculated values are EOM-CCSD using a comparable basis set. Reference 8. c Reference 9. d Reference 26. e These two states have mixed CT and double-excitation character. b
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While it is not the goal of this work to determine the absorption threshold of water molecules in clusters, it is useful to compare the results presented here with previous work on this subject, both computational and experimental. Computational studies of the lowest valence electronic transitions in small water clusters (dimers and pentamers), performed at a similar level of theory to the present study (EOM-CCSD), give energies for the lowest excited state in the range of 7.0–8.3 eV,27–29 a range whose higher end corresponds quite well with our lowest energy excitations on water, that is, 7.9–8.3 eV. Published values for the vertical band gap of water from experiment range from about 7.8 eV to 10.0 eV,30, 31 though there is evidence of ionization in liquid water at lower energies.30 The lowest values for the CC(2,3) energies of the doubly excited states for each cluster fall toward the lower portion of this range. Regarding the main thrust of this work, however, the excitations of water will have little effect on the CT transition of OH, as a number of CT transitions lie at significantly lower energies. Looking first at the A ← X transition energies, it is clear that, by and large, as cluster size increases, this transition energy decreases. This behavior has been reported previously,8, 9 and is readily attributed to the increase in the polarizability of the cluster as the number of water molecules increases. It is interesting to note that the A ← X transition energies for clusters OH-4WF and OH-4WG , where the OH participates in hydrogen bonds with three different water molecules, drop more than 0.3 eV below the energies for the same transition even for the other OH-(H2 O)4 clusters. While having more water molecules present decreases the transition energy, close proximity causes the energy to drop even further. On the other hand, for the OH-3WD complex, where the OH is also hydrogen bonded to three water molecules, there is no comparable energy lowering of the A ← X transition relative to the other OH-3W complexes. Turning attention to the CT transitions, it is apparent that the number of these states proliferates as the number of water molecules in the cluster increases. Previous studies8, 9 did not attempt high-order ab initio calculation for more than one CT state, so this observation is new. The CT states that are relevant to the absorption spectrum of OH in aqueous solution are going to be those of lowest energy. The lowest CT states involve MOs constructed from non-bonding 2p orbitals on oxygen atoms in water molecules that are just one hydrogen bond away from the OH radical. The OH radical in all OH(H2 O)2 structures, the first three OH-(H2 O)3 structures, and the first five OH-(H2 O)4 structures have two nearest-neighbor H2 O molecules, so the presence of two low-energy CT states makes sense. Further, in structures OH-3WD , OH-4WF and OH-4WG , where the OH radical hydrogen bonds with three different water molecules, three low-lying CT states are observed. In larger clusters, higher CT states are formed by excitations from non-bonding orbitals of water molecules that are two hydrogen bonds away. Another group of the CT states, in the energy range of ∼8–10 eV, is formed by electron transfer from σ orbitals in water molecules. Thus, the total number of CT states increases with increase of the number of water molecules in the cluster.
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Generally, as the number of H2 O molecules in the cluster increases, the energy of the lowest CT state decreases, though there are a few exceptions among the clusters studied. The lowest energy for the first CT state calculated, for OH-4WD , is 5.657 eV, coming in just 0.26 eV above the peak of the CT feature observed in the aqueous OH spectrum at 5.39 eV. The general trend is explained by the increasing polarizability of the cluster with the increasing number of water molecules, just as in the case of the A ← X transition energies. Additionally, the CT states are known to be strongly stabilized by water solvent. However, much larger water clusters should be considered to get convergence on this stabilization effect. We leave this question to our future work. In several of the clusters considered (OH-1WB , OH2WC , and OH-3WD ), the lowest CT energies are well below those of all other structures regardless of size. It is likely that these low energy CT states are due to a structural aspect that these clusters share. Indeed, in these structures, the OH radical is in the same plane as the H2 O molecule involved in that lowest energy charge transfer state. The donor MO is exactly parallel with the acceptor MO; both are perpendicular to the plane these atoms share. This condition is not satisfied in the other clusters presented in this study. The optimal relative orientation of the donor and acceptor MOs results in a reduction in the transition energy. This also explains why the structure OH-2WC does not have a pair of CT states at low energy despite the fact that it has two adjacent water molecules. The donor orbital for the second CT transition in structure OH2WC includes approximately equal contributions from both water molecules, each from orbitals oriented to be parallel with the plane of the ring, which is perpendicular to the acceptor orbital on OH (see Figure 6). This orientation is highly unfavorable to the transition, leading to an increase in the energy for that particular CT state.22 The unfavorable geometry also results in a very small oscillator strength for this transition. Figure 9 displays the spectra for the various clusters studied here as the oscillator strength of a transition versus its wavelength. The four plots collect the spectra of different sized clusters: (a) bare OH and OH-1W; (b) OH-2W; (c) OH3W; and (d) OH-4W. The A ← X transitions are all found at longer wavelength, to the right, while the charge-transfer transitions occur at shorter wavelength. The trend toward lower transition energy, and hence longer wavelength, as the number of water molecules in a cluster increases is clear in this figure, as are the anomalies to this trend mentioned above: OH-1WB in plot (a) (green); OH-2WC in plot (b) (green); and OH-3WD in plot (c) (violet). A few other trends are apparent as well. First, the oscillator strength of the CT transitions increase, on average, as the number of water molecules increases. Second, the oscillator strength of CT transitions at shorter wavelength drops. This latter observation is presumably caused by the reduction in overlap between donor and acceptor MOs due to either unfavorable geometry, or greater distance between the two. We can imagine that as the number of H2 O molecules in the cluster increases, the number of CT states continues to proliferate, and their oscillator strengths continue to grow. It is expected that the CT states become further stabilized and
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Additional enhancement in intensity and red-shift of the CT band might arise due to transient hemibonded structures populated at finite temperatures. While not local minima of OH-water clusters, these hemibonded structures have favorable orbital overlap ensuring intense low-lying CT states and are thought to be major contributors to the observed near-UV spectrum.9 As the conditions of bulk water are approached, it is reasonable to visualize that the CT states form a band, one whose structure could resemble the absorption band of the OH radical dissolved in water. It is plausible that the shape of this CT absorption band is determined by a combination of several effects, such as polarization of the solvent, hole delocalization, and the presence of non-equilibrium hemibonded OH-H2 O structures at finite temperatures. The relative significance of these effects will be explored in future work. IV. CONCLUSION
Results are presented for EOM-IP-CC calculations on a variety of OH-H2 O, OH-(H2 O)2 , OH-(H2 O)3 , and OH(H2 O)4 clusters in order to study their charge transfer states. One new structure for OH-(H2 O)3 , and five new structures for OH-(H2 O)4 clusters were discovered in the process. The nature of the excited states was determined by analysis of the orbitals involved in those transitions. The general trends observed were that the intensity and the total number of CT states increased, as the number of H2 O molecules in the cluster increased. The proliferation of CT states with cluster size implies that the CT states form a band of delocalized hole states in bulk water. It is expected that as the conditions of bulk water are approached, this CT band will resemble the experimentally observed absorption peak associated with the OH charge-transfer band in water. Continuing work on OH aims to confirm these hypotheses, and to further investigate the dynamics of the excited CT state. FIG. 9. Plots of transition oscillator strength versus transition wavelength for (a) OH and OH-1W dimers; (b) OH-2W clusters; (c) OH-3W clusters; and (d) OH-4W clusters.
red-shifted due to polarization of the solvent water. While the lowest energy CT states involve H2 O molecules that are nearest neighbors to the OH, we observe that some of the donor MOs involved have contributions from more than one H2 O molecule, and are hence delocalized. The MOs associated with higher energy CT transitions generally display even greater delocalization as linear combinations of oxygen p orbitals on the various water molecules in the complexes are involved. Analyzing the clusters containing three and four water molecules shows that delocalization of the CT states is spread beyond the first hydration shell of OH; however, these CT states generally lie 1 eV or more above the low ones. Still, even taking only the low-lying CT states into account, the CT absorption of hydrated OH may be due to a band of delocalized hole states in liquid water. There have been recent efforts to understand delocalized hole states in liquid water,28, 29, 32, 33 and further progress may help in the understanding of CT dynamics of hydrated OH.
ACKNOWLEDGMENTS
G.J.H. wishes to thank Edinboro University of Pennsylvania for granting a 6 month sabbatical leave. L.V.S. acknowledges support from the National Science Foundation (Grant No. CHE-0955419). 1 W.
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J. Chem. Phys. 141, 104315 (2014) P. Steele, V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C. Byrd, H. Daschel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C.-P. Hsu, G. Kedziora, R. Z. Khaliullin, P. Klunzinger, A. M. Lee, M. S. Lee, W.-Z. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock III, W. Zhang, A. T. Bell, A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel, W. J. Hehre, H. F. Schaefer III, J. Kong, A. I. Krylov, P. M. W. Gill, and M. Head-Gordon, Phys. Chem. Chem. Phys. 8, 3172 (2006). 24 B. M. Bode and M. S. Gordon, J. Mol. Graphics Model. 16, 133 (1998). 25 J. R. Schmidt and W. F. Polik, WebMO Enterprise, version 13.1, WebMO llc, Holland, MI, USA, see http://www.webmo.net (accessed September 2013). 26 K.-P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand, New York, U.S.A., 1979). 27 D. M. Chipman, J. Chem. Phys. 122, 044111 (2005). 28 P. Cabral do Couto and D. M. Chipman, J. Chem. Phys. 132, 244307 (2010). 29 P. Cabral do Couto and D. M. Chipman, J. Chem. Phys. 137, 184301 (2012). 30 A. Bernas, C. Ferradini, and J.-P. Jay-Gerin, Chem. Phys. 222, 151 (1997). 31 J. V. Coe, A. D. Earhart, M. H. Cohen, G. J. Hoffman, H. W. Sarkas, and K. H. Bowen, J. Chem. Phys. 107, 6023 (1997). 32 O. Marsalek, C. G. Elles, P. A. Pieniazek, E. Pluhaˇrová, J. VandeVondele, S. E. Bradforth, and P. Jungwirth, J. Chem. Phys. 135, 224510 (2011). 33 O. Svoboda, M. Onˇ cák, and P. Slavíˇcek, J. Chem. Phys. 135, 154301 (2011); 135, 154302 (2011).
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THE JOURNAL OF CHEMICAL PHYSICS 141, 104315 (2014)
Excited states of OH-(H2 O)n clusters for n = 1–4: An ab initio study Gerald J. Hoffman,1 Pradeep K. Gurunathan,2 Joseph S. Francisco,2 and Lyudmila V. Slipchenko2,a) 1
Department of Chemistry, Edinboro University of Pennsylvania, 230 Scotland Road, Edinboro, Pennsylvania 16444, USA 2 Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
(Received 12 June 2014; accepted 25 August 2014; published online 11 September 2014) Equation of motion coupled cluster calculations were performed on various structures of OH in clusters with one, two, three, and four water molecules to determine the energies of valence and charge transfer states. Motivation for these calculations is to understand the absorption spectrum of OH in water. Previous calculationson these species have confirmed that the longer wavelength transition observed is due to the A(2 ) ← X(2 ) valence transition, while the shorter wavelength transition is due to a charge-transfer from H2 O to OH. While these previous calculations identified the lowest energy charge-transfer state, our calculations have included sufficient states to identify additional solvent-to-solute charge transfer states. The minimum energy structures of the clusters were determined by application of the Monte Carlo technique to identify candidate cluster structures, followed by optimization at the level of second-order Møller-Plesset perturbation theory. Calculations were performed on two structures of OH-H2 O, three structures of OH-(H2 O)2 , four structures of OH-(H2 O)3 , and seven structures of OH-(H2 O)4 . Confirming previous calculations, as the number of water molecules increases, the energies of the excited valence and charge-transfer states decrease; however, the total number of charge-transfer states increases with the number of water molecules, suggesting that in the limit of OH in liquid water, the charge-transfer states form a band. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894772] I. INTRODUCTION
The hydroxyl radical, OH, plays a fundamentally important role in oxidative chemical processes in the atmosphere.1 However, in order to accurately model its behavior in the atmospheric environment, either for the purposes of measurement or to deduce reaction mechanisms, it is necessary to understand how it interacts with water.2–6 OH may interact with just one,2 or a few water molecules,3–6 or it may dissolve in a water droplet, which would produce an environment for the OH essentially identical to that of bulk water. The study of OH in bulk water has a long history. Interestingly, its absorption spectrum is still a topic of active research. Two particular features are observed in this spectrum: a shoulder that appears under certain conditions around 4.00 eV (310 nm), and a broad peak centered at 5.39 eV (230 nm).7 The shoulder is generally believed to be due to the A ← X valence transition familiar from the spectroscopy of the gas-phase radical, while the broad peak has been assigned to a charge transfer between the water and the OH. Two recent computational studies have shown that the transition next in energy above the A ← X transition is, in fact, a charge transfer (CT) transition, where the electron jumps from water to the OH radical, thus producing a hydroxide anion.8, 9 The objective of the present study is to obtain a more realistic and complete picture of the CT states in OH-water clusters, leading to a better understanding of such states in bulk a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/141(10)/104315/9/$30.00
water. Multiple structures for clusters of OH with two, three, and four water molecules were determined; some of these structures have not been reported previously. Calculations were performed on these cluster structures to obtain excited state energies, including CT states. In the previous studies,8, 9 only the lowest energy CT transition was calculated. However, when there are multiple water molecules present, there are multiple possible CT transitions. Indeed, even when OH is clustered with just a single H2 O, that H2 O may transfer an electron from one of several molecular orbitals. As the number of such states grows with the size of the cluster, one can imagine the formation of a CT band. The nature of such a band is still to be investigated, but recognizing the possible existence of this band may change the understanding of electronic and photochemical phenomena in liquid water. II. COMPUTATIONAL DETAILS
Except for the OH-H2 O dimers, structures for clusters were identified by Monte Carlo sampling of OH with the specified number of water molecules, followed by structure optimization using second order Møller-Plesset theory (MP2)10 on an unrestricted Hartree-Fock (UHF) reference wavefunction. The Monte Carlo computations were performed using the GAMESS computational chemistry software package.11 To speed up Monte Carlo simulations, the molecular clusters were described at a hybrid quantum-classical level. In particular, OH was treated using density functional theory (DFT) with the B3LYP exchangecorrelation functional12 and Dunning-Hay double-zeta
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basis sets with polarization functions.13 Water molecules were represented by fragments in the effective fragment potential (EFP) framework.14 DFT-based EFP1 water potentials were used.15 For the MP2 optimizations, the 6-311++G** basis set was used.16 This technique was used previously to identify candidate structures for O3 -(H2 O)n clusters, with n = 1–4.17 As for the OH-H2 O dimers, only two of the many structures identified in previous work were studied: the lowest energy structure with OH as proton donor in a hydrogen bond, and the lowest energy structure with H2 O as proton donor in a hydrogen bond. The total binding energy of each cluster was calculated at the level of MP2; no correction was made for basis set superposition error. Once structures were determined, excited state energies were computed by applying equation of motion coupled cluster methodology (EOM CC). Specifically, ionization potential (IP) versions of EOM-CC with single and double excitations (EOM-IP-CCSD)18–20 and with single, double, and triple excitations (EOM-IP-CC(2,3))21 were employed, again using the 6-311++G** basis set. In the IP technique, an additional electron is added to the cluster, making the hydroxyl radical the hydroxide ion, and closing its shell. The ionization potentials (IPs) for electrons from each occupied orbital (as many as desired, depending on computational capacity) are then calculated. The differences between each of these IPs and the lowest IP (which corresponds to the energy required to create the ground state of the radical from the ion) then give the energies of the excited states. EOM-IP-CC techniques provide a more balanced description of radicals, as spin-contamination, which often causes the accuracy of standard EOM-CC to deteriorate for open-shells, is avoided. For the OH-H2 O clusters, the first 10 electronic states were calculated; for the OH(H2 O)2 clusters, the first 15 electronic states were calculated; for the OH-(H2 O)3 clusters, 16 electronic states were calcu-
FIG. 1. Structures of OH-H2 O considered in this study.
lated; for the OH-(H2 O)4 clusters, 20 electronic states were calculated. However, EOM-CC(2,3) was not applied to the latter clusters. Finally, oscillator strengths for the transitions of interest were calculated at the level of EOM-IP-CCSD. The EOM-IP-CCSD technique has been previously applied to the OH-H2 O dimer, in the interest of investigating the effects of hemibonding between the moieties on CT transition energies; however, still, only the first CT state was investigated.22 All excited state calculations in this work, as well as calculation of the MP2 binding energies, were performed using the Q-Chem electronic structure package.23 Images of cluster structures were made using MacMolPlt.24 Images of molecular orbitals were constructed using WebMO.25 III. RESULTS AND DISCUSSION
The structures of OH-H2 O studied in this work are shown in Figure 1. These particular structures were chosen from the numerous previously calculated structures of this dimer because they are the most stable hydrogen-bonded structures, OH-1WA with OH as the hydrogen donor, and OH-1WB with H2 O as the hydrogen donor. Despite published structures for these two species to high levels of theory, we are using the MP2 optimized structures for the sake of consistency with our treatment of all other clusters in this study. Binding energies for all the clusters studied are collected in Table I.
TABLE I. Total and relative MP2 binding energies (in kcal mol−1 ) of the clusters studied. Relative energya OH-(H2 O)n−1 + H2 O → OH-(H2 O)n
Relative energyb OH-(H2 O)n−2 + (H2 O)2 → OH-(H2 O)n
Total energy
Previous calculation
OH-1WA OH-1WB
6.66 3.71
6.1c , 5.5d 3.2c , 3.8d
OH-2WA OH-2WB OH-2WC
16.14 15.82 11.01
14.1d 13.9d 9.7d
9.48 9.16 4.35
10.09 9.77 4.95
OH-3WA OH-3WB OH-3WC OH-3WD
28.86 28.44 22.72 20.46
25.60d ... 20.1d 18.9d
12.71 12.30 6.58 4.32
16.14 15.72 10.00 7.74
OH-4WA OH-4WB OH-4WC OH-4WD OH-4WE OH-4WF OH-4WG
39.64 37.03 35.00 34.96 34.77 34.27 33.98
34.80d ... ... ... ... 30.35d ...
10.78 8.17 6.14 6.10 5.91 5.41 5.12
17.44 14.83 12.80 12.76 12.57 12.07 11.78
Cluster
a
The lowest energy OH-(H2 O)n−1 structures are used for calculating relative energies. The lowest energy OH-(H2 O)n−2 structures are used for calculating relative energies. Binding energy of (H2 O)2 is 6.06 kcal/mol. c Reference 9; CCSD(T)/6-311(2+)G∗ including correction for BSSE. d Reference 6; DFT energies at the level of MPW1PW91/aug-cc-pVQZ//MPW1PW91/aug-cc-pVDZ. b
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FIG. 2. Structures of OH-(H2 O)2 considered in this study.
MP2 results compare well with previous calculations for these dimers, both at the level of CCSD(T)9 and DFT,6 to within a few tenths of a kcal mol−1 . Structures for OH-(H2 O)2 clusters are shown in Figure 2; all of these structures have been reported previously.4, 6 Structure OH-2WA has the dangling hydrogens on the waters pointing toward opposite sides of the ring while structure OH-2WB has them on the same side of the ring. Structure OH-2WC is significantly different from the other 2W clusters, with one H2 O molecule acting as a hydrogen bond acceptor to both OH and the other H2 O. This double hydrogen bond acceptor H2 O has both its hydrogens pointing outward, away from the ring; this molecule occupies a plane perpendicular to the plane of the ring. MP2 binding energies for these clusters, shown in Table I, agree to within 2 kcal mol−1 with previous DFT calculations6 and display the same trend for the three structures. Not surprisingly, relative binding energies of addition of a water molecule to OH-(H2 O)n−1 cluster, i.e., OH-(H2 O) + H2 O → OH-(H2 O)2 , also show dramatic decrease in the case of OH-2WC cluster, indicating the destabilization of the hydrogen bonded network in this cluster. Structures for OH-(H2 O)3 clusters are shown in Figure 3; of these four structures, only OH-3WB has not been previously reported.4, 6 Structure OH-3WB shares the fourmembered hydrogen-bonded ring of OH-3WA , but the orientations of the dangling hydrogens are no longer alternating. Structure OH-3WC is a variation of structure OH-2WA with an additional water molecule accepting a hydrogen bond from an H2 O in the ring. It should not be a surprise that re-
FIG. 3. Structures of OH-(H2 O)3 considered in this study.
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sults of calculations on this particular structure share much in common with those of structures OH-2WA and OH-2WB . In structure OH-3WD , unlike the other 3W structures considered, OH forms three hydrogen bonds with surrounding water molecules, more closely mimicking the behavior of OH in bulk water. Comparison of MP2 binding energies in Table I with previously calculated DFT6 binding energies for OH3WA , OH-3WC , and OH-3WD again shows agreement in the trend, with discrepancy on the order of 3 kcal mol−1 . Relative binding energies of OH-3WA and OH-3WB clusters, in which the third water builds two hydrogen bonds, are ∼12 kcal mol−1 that approximately corresponds to the energy of two hydrogen bonds. Relative binding energies in OH-3WC and OH-3WD clusters are only 4–6 kcal mol−1 , which can be rationalized by the fact that the third water builds only one hydrogen bond in these clusters. Another observation is that relative binding energies in square-like OH-3WA and OH3WB structures are higher than the corresponding energies in triangular-like OH-2WA and OH-2WB clusters. This is because square-like water complexes experience more optimal hydrogen bonds than rather constrained triangular water clusters. The structures for the seven OH-(H2 O)4 clusters considered in this study are found in Figure 4. Only structures OH-4WA and OH-4WF have been reported previously.4, 6 The MP2 total binding energies for these clusters are found in Table I, and compared with DFT values6 for the two previously reported structures. The structures are ordered in terms of decreasing binding energies, though they could also be categorized according to structural similarity. Structure OH4WA is the unique pentagonal structure, with the highest total and relative binding energies. Structures OH-4WC , OH4WD , and OH-4WE are based upon square OH-(H2 O)3 structures, with an additional water accepting a hydrogen bond from one of the dangling hydrogens on the water molecules making up the square. The relative binding energies in these
FIG. 4. Structures of OH-(H2 O)4 considered in this study.
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clusters are ∼6 kcal/mol that corresponds to strength of a single newly formed H-bond. The square portions of structures OH-4WC and OH-4WD are clearly based on structure OH3WB , while the square portion of OH-4WE does not resemble either OH-3WA or OH-3WB . Structures OH-4WB , OH-4WF , and OH-4WG similarly have the OH in a square structure with three water molecules, but the fourth water molecule forms two hydrogen bonds with two adjacent moieties in the square (one as hydrogen donor, one as accepter). In OH-4WB , the fourth water hydrogen bonds with two adjacent waters with relative binding energy of ∼8 kcal/mol, while the OH lies in a different part of the square. In both OH-4WF and OH4WG , OH acts as hydrogen bond acceptor to the fourth water molecule, such that the OH participates in hydrogen bonding with three water molecules. Relative binding energies of adding the fourth water in these clusters are almost 3 kcal/mol lower than in OH-4WB , in accord with observation that OH is a weaker hydrogen bond acceptor than a water. The difference between OH-4WF and OH-4WG lies in the orientations of the dangling hydrogens of the two water molecules in the square not participating in the interactions with the fourth, bridging water molecule. These two structures are important in understanding the effect of the number of hydrogen bonds to the OH on the CT states. Like OH-3WD , the OHs in these two structures form three hydrogen bonds with adjacent water molecules, as they would in bulk water. The structures investigated here are not an exhaustive list of possible cluster structures; a number of known structures for these clusters were not included in this investigation.6 However, this set of structures is sufficiently broad to investigate the electronic properties of OH in a variety of water cluster environments. The EOM-IP technique indicates for each state which of the molecular orbitals is being ionized. The nature of each state was determined by observing the shape and location of the principal contributing molecular orbital (MO) being ionized. The MOs with the greatest contribution to each ionization for representative clusters can be observed in Figures 5 through 8. Figure 5 depicts the MOs for dimers OH1WA and OH-1WB . Figure 6 shows MOs for clusters OH-
FIG. 5. Orbitals involved in the lowest transitions in (a) OH-1WA and (b) OH-1WB . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right. States resulting from the transition are denoted below each donor orbital.
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FIG. 6. Orbitals involved in the first three UV transitions in (a) OH-2WA and (b) OH-2WC . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right. (The fully occupied π orbital on OH has been excluded from this figure.) States resulting from the transition are denoted below each donor orbital.
2WA and OH-2WC ; the MOs for OH-2WB are not displayed because they are similar to those for OH-2WA . Figure 7 represents the MOs for clusters OH-3WA and OH-3WD ; the MOs for cluster OH-3WB resemble those of OH-3WA , and the MOs for cluster OH-3WC resemble those of OH-2WA . Figure 8 depicts the MOs for clusters OH-4WA and OH-4WF ; the MOs for clusters OH-4WB , OH-4WC , OH-4WD , and OH4WE resemble those of OH-3WA, while MOs for cluster OH4WG resemble those of OH-4WF . States resulting from the transition are denoted below each donor orbital. The leftmost MO in each figure is the half-filled OH π orbital of the ground state of the cluster; this MO is the acceptor orbital for the important transitions in each cluster. The orbitals to the right of this MO have IPs that increase from left to right, and are labeled according to what kind of transition connects them to the acceptor MO. In Figure 5, the first two donor orbitals are located on the OH: the orthogonal nonbonding π orbital, normally fully occupied in the ground state and nearly degenerate with the acceptor MO; and then the σ MO that bonds the oxygen to the hydrogen. (In Figures 6–8, the image of the nearly degenerate fully occupied π orbital has been excluded as it has no relevance to
FIG. 7. Orbitals involved in the first three UV transitions in (a) OH-3WA and (b) OH-3WD . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right.
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FIG. 8. Orbitals involved in the first three UV transitions in (a) OH-4WA and (b) OH-4WF . The leftmost orbital is the acceptor orbital on the OH. The orbitals to the right are the donor orbitals, ordered in increasing energy difference (from the acceptor orbital) from left to right. (The fully occupied π orbital on OH has been excluded from this figure.) States resulting from the transition are denoted below each donor orbital.
our focus: the CT transitions.) The transition between the σ MO and the acceptor MO is the A ← X transition. Note in the figures that there is a small amount of amplitude on the oxygen accepting the hydrogen bond from the OH in the larger clusters, lending a small amount of CT character to this transition. The MOs found to the right of the OH orbitals in the figures are all located principally on the water molecules of the clusters; transitions between these and the acceptor MO give rise to full-fledged CT states. The donor MOs on water that participate in the lowest energy CT transitions consist of nonbonding oxygen 2p orbitals perpendicular to the H2 O
molecular plane; these correspond to the 1b1 orbital in the bare H2 O molecule. Note also that some of these donor MOs show significant amplitude on more than one H2 O molecule, suggesting significant electron delocalization. Transition energies calculated using EOM-IP-CCSD and EOM-IP-CC(2,3) are reported in Tables II–IV. In each table, the first row gives the energy splitting between the two components of 2 state of OH. The next row gives the energy of 2 the A( ) state of OH relative to the ground state. The section below displays the energies of the CT states for each cluster. The bottom section lists the energies of the excited electronic states originating on water molecules. Formally these states are double excitations in the EOM-IP formalism, with the double excitation consisting of ionization of one of the π orbitals on OH− , and valence excitation of an electron in one of the water molecules. It is interesting that not all the energies of the listed doubly excited states lie above those of the listed CT states, particularly in the case of CC(2,3) (Table IV). In comparing energy values between Tables II and IV, we see that the energies of all the corresponding states are within a few hundredths of an eV except for the excitations on water molecules. The application of CC(2,3) greatly lowers the energies of the water excitations. Due to their doubly excited character, these states may be significantly in error at the EOM-IP-CCSD level, but become more accurately described with inclusion of triple amplitudes in EOM-IP-CC(2,3). At the CC(2,3) level, the higher-energy CT states interleave with the water excited states. This is why there are fewer CT states listed in Table IV than in Table II.
TABLE II. EOM-IP-CCSD transition energies (eV) for OH and OH-(H2 O)n , for n = 1, 2, and 3. OH 2
A (2 ) Previous calculationa Expt.d CT
Previous calculationa Excitations on water
4.226 4.24b 4.31c 4.05 ...
OH-1WA
OH-1WB
OH-2WA
OH-2WB
OH-2WC
OH-3WA
OH-3WB
OH-3WC
OH-3WD
0.011 3.882 3.89b 3.85c
0.091 4.258
0.120 3.719 3.74b
0.125 3.738
0.027 3.949
0.177 3.529 3.65b
0.183 3.608
0.129 3.514
0.200 3.931
4.30c
7.759 10.020 14.122
5.002 7.353 11.221
6.325 6.354 8.263 8.958 12.319 12.971
6.128 6.517 8.324 8.883 12.284 12.993
5.687 7.607 8.128 10.016 11.992 14.242
6.033 6.154 7.004 8.090 8.422 9.787 12.081 12.534 13.519 6.62b
6.030 6.063 7.052 8.140 8.490 9.772 12.091 12.619 13.548
6.007 6.244 7.994 8.611 9.175 11.180 12.303 12.838
4.798 5.763 6.113 7.160 7.750 8.611 10.997 11.989 12.555
14.062 14.154 14.167 14.463 14.524 14.531
13.633 13.683 13.802 13.974 14.339 14.490
14.372 14.554 14.837
14.264 14.380 14.465 14.483
14.015 14.107 14.122 14.202 14.204
13.523 13.632 13.797 14.096
7.37b 14.123 14.173 14.315 14.864
6.89b 5.43c 13.443 13.552 13.884 14.109
14.119 14.209 14.226 14.502 14.576 14.822
a
All calculated values are EOM-CCSD using a comparable basis set. Reference 8. Reference 9. d Reference 26. b c
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TABLE III. EOM-IP-CCSD transition energies (eV) for OH and OH-(H2 O)4 . OH-4WA
OH-4WB
OH-4WC
OH-4WD
OH-4WE
OH-4WF
OH-4WG
0.176 3.467 3.50a 5.997 6.067 7.235 7.377 8.136 8.241 9.478 10.453 12.015 12.564 13.658 13.858 14.300 14.416 14.540 14.549 14.574
0.181 3.362
0.150 3.579
0.194 3.381
0.192 3.310
0.254 3.029
0.244 3.016
5.962 6.134 7.360 7.460 8.112 8.348 9.808 10.120 11.951 12.124 13.822 14.081 14.236 14.247 14.317 14.415 14.415
5.767 6.107 6.967 7.708 8.435 8.951 9.710 10.775 12.283 12.593 13.447
5.657 6.063 6.982 7.982 8.237 8.962 9.642 11.125 12.075 12.525 13.474
5.767 6.000 7.026 7.910 8.236 8.847 9.642 11.020 12.055 12.458 13.555
14.188 14.199 14.364 14.189 14.409 14.425
14.221 14.223 14.242 14.358 14.383 14.414
14.164 14.214 14.218 14.272 14.382 14.431
5.758 5.932 6.307 6.697 7.596 8.086 8.641 9.410 11.804 11.978 12.660 13.189 14.159 14.252 14.262 14.358 14.471
5.714 5.955 6.303 6.686 7.646 8.083 8.635 9.326 11.778 11.992 12.643 13.174 14.170 14.269 14.279 14.360 14.472
2
A (2 ) Previous calculation CT
Excitations on water
a
Calculated values are EOM-CCSD using a comparable basis set from Ref. 8.
TABLE IV. EOM-IP-CC(2,3) transition energies (eV) for OH and OH-(H2 O)n , for n = 1, 2, and 3. OH 2
A (2 ) Previous calculationa Expt.d CT
Previous calculationa
4.248 4.24b 4.31c 4.05 ...
OH-1WA
OH-1WB
OH-2WA
OH-2WB
OH-2WC
OH-3WA
OH-3WB
OH-3WC
OH-3WD
0.019 3.846 3.89b 3.85c
0.082 4.236
0.125 3.695 3.74b
0.130 3.713
0.028 3.911
0.172 3.501 3.65b
0.179 3.577
0.136 3.491
0.188 3.902
6.271 6.412 8.271
6.114 6.542 8.319
5.694 7.665 8.154
5.980 6.209 7.049 8.072 8.412
5.998 6.103 7.093 8.107 8.464e 8.519e
6.079 6.182 8.033 8.566
4.821 5.841 6.080 7.181 7.800
8.255 8.265 8.346 8.394 8.395 8.418 8.444 8.464e 8.519e
8.136 8.142 8.142 8.179 8.265 8.266 8.356 8.572 8.611
7.839
4.30c 5.009 7.356
7.37b
6.89b
6.62b
5.43c Excitations on water
8.133 8.153 8.170 8.185 8.616 8.640
7.725 7.773 8.123 8.147 8.448
8.247 8.292 8.350 8.396 8.455 8.467 8.523 8.691 8.735
8.168 8.214 8.337 8.362 8.377 8.470 8.477 8.592 8.680
7.953 8.006 8.013 8.254 8.347 8.446 8.476 8.488 8.519
8.342 8.347 8.354 8.390 8.419 8.469 8.541 8.596
a
All calculated values are EOM-CCSD using a comparable basis set. Reference 8. c Reference 9. d Reference 26. e These two states have mixed CT and double-excitation character. b
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While it is not the goal of this work to determine the absorption threshold of water molecules in clusters, it is useful to compare the results presented here with previous work on this subject, both computational and experimental. Computational studies of the lowest valence electronic transitions in small water clusters (dimers and pentamers), performed at a similar level of theory to the present study (EOM-CCSD), give energies for the lowest excited state in the range of 7.0–8.3 eV,27–29 a range whose higher end corresponds quite well with our lowest energy excitations on water, that is, 7.9–8.3 eV. Published values for the vertical band gap of water from experiment range from about 7.8 eV to 10.0 eV,30, 31 though there is evidence of ionization in liquid water at lower energies.30 The lowest values for the CC(2,3) energies of the doubly excited states for each cluster fall toward the lower portion of this range. Regarding the main thrust of this work, however, the excitations of water will have little effect on the CT transition of OH, as a number of CT transitions lie at significantly lower energies. Looking first at the A ← X transition energies, it is clear that, by and large, as cluster size increases, this transition energy decreases. This behavior has been reported previously,8, 9 and is readily attributed to the increase in the polarizability of the cluster as the number of water molecules increases. It is interesting to note that the A ← X transition energies for clusters OH-4WF and OH-4WG , where the OH participates in hydrogen bonds with three different water molecules, drop more than 0.3 eV below the energies for the same transition even for the other OH-(H2 O)4 clusters. While having more water molecules present decreases the transition energy, close proximity causes the energy to drop even further. On the other hand, for the OH-3WD complex, where the OH is also hydrogen bonded to three water molecules, there is no comparable energy lowering of the A ← X transition relative to the other OH-3W complexes. Turning attention to the CT transitions, it is apparent that the number of these states proliferates as the number of water molecules in the cluster increases. Previous studies8, 9 did not attempt high-order ab initio calculation for more than one CT state, so this observation is new. The CT states that are relevant to the absorption spectrum of OH in aqueous solution are going to be those of lowest energy. The lowest CT states involve MOs constructed from non-bonding 2p orbitals on oxygen atoms in water molecules that are just one hydrogen bond away from the OH radical. The OH radical in all OH(H2 O)2 structures, the first three OH-(H2 O)3 structures, and the first five OH-(H2 O)4 structures have two nearest-neighbor H2 O molecules, so the presence of two low-energy CT states makes sense. Further, in structures OH-3WD , OH-4WF and OH-4WG , where the OH radical hydrogen bonds with three different water molecules, three low-lying CT states are observed. In larger clusters, higher CT states are formed by excitations from non-bonding orbitals of water molecules that are two hydrogen bonds away. Another group of the CT states, in the energy range of ∼8–10 eV, is formed by electron transfer from σ orbitals in water molecules. Thus, the total number of CT states increases with increase of the number of water molecules in the cluster.
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Generally, as the number of H2 O molecules in the cluster increases, the energy of the lowest CT state decreases, though there are a few exceptions among the clusters studied. The lowest energy for the first CT state calculated, for OH-4WD , is 5.657 eV, coming in just 0.26 eV above the peak of the CT feature observed in the aqueous OH spectrum at 5.39 eV. The general trend is explained by the increasing polarizability of the cluster with the increasing number of water molecules, just as in the case of the A ← X transition energies. Additionally, the CT states are known to be strongly stabilized by water solvent. However, much larger water clusters should be considered to get convergence on this stabilization effect. We leave this question to our future work. In several of the clusters considered (OH-1WB , OH2WC , and OH-3WD ), the lowest CT energies are well below those of all other structures regardless of size. It is likely that these low energy CT states are due to a structural aspect that these clusters share. Indeed, in these structures, the OH radical is in the same plane as the H2 O molecule involved in that lowest energy charge transfer state. The donor MO is exactly parallel with the acceptor MO; both are perpendicular to the plane these atoms share. This condition is not satisfied in the other clusters presented in this study. The optimal relative orientation of the donor and acceptor MOs results in a reduction in the transition energy. This also explains why the structure OH-2WC does not have a pair of CT states at low energy despite the fact that it has two adjacent water molecules. The donor orbital for the second CT transition in structure OH2WC includes approximately equal contributions from both water molecules, each from orbitals oriented to be parallel with the plane of the ring, which is perpendicular to the acceptor orbital on OH (see Figure 6). This orientation is highly unfavorable to the transition, leading to an increase in the energy for that particular CT state.22 The unfavorable geometry also results in a very small oscillator strength for this transition. Figure 9 displays the spectra for the various clusters studied here as the oscillator strength of a transition versus its wavelength. The four plots collect the spectra of different sized clusters: (a) bare OH and OH-1W; (b) OH-2W; (c) OH3W; and (d) OH-4W. The A ← X transitions are all found at longer wavelength, to the right, while the charge-transfer transitions occur at shorter wavelength. The trend toward lower transition energy, and hence longer wavelength, as the number of water molecules in a cluster increases is clear in this figure, as are the anomalies to this trend mentioned above: OH-1WB in plot (a) (green); OH-2WC in plot (b) (green); and OH-3WD in plot (c) (violet). A few other trends are apparent as well. First, the oscillator strength of the CT transitions increase, on average, as the number of water molecules increases. Second, the oscillator strength of CT transitions at shorter wavelength drops. This latter observation is presumably caused by the reduction in overlap between donor and acceptor MOs due to either unfavorable geometry, or greater distance between the two. We can imagine that as the number of H2 O molecules in the cluster increases, the number of CT states continues to proliferate, and their oscillator strengths continue to grow. It is expected that the CT states become further stabilized and
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Additional enhancement in intensity and red-shift of the CT band might arise due to transient hemibonded structures populated at finite temperatures. While not local minima of OH-water clusters, these hemibonded structures have favorable orbital overlap ensuring intense low-lying CT states and are thought to be major contributors to the observed near-UV spectrum.9 As the conditions of bulk water are approached, it is reasonable to visualize that the CT states form a band, one whose structure could resemble the absorption band of the OH radical dissolved in water. It is plausible that the shape of this CT absorption band is determined by a combination of several effects, such as polarization of the solvent, hole delocalization, and the presence of non-equilibrium hemibonded OH-H2 O structures at finite temperatures. The relative significance of these effects will be explored in future work. IV. CONCLUSION
Results are presented for EOM-IP-CC calculations on a variety of OH-H2 O, OH-(H2 O)2 , OH-(H2 O)3 , and OH(H2 O)4 clusters in order to study their charge transfer states. One new structure for OH-(H2 O)3 , and five new structures for OH-(H2 O)4 clusters were discovered in the process. The nature of the excited states was determined by analysis of the orbitals involved in those transitions. The general trends observed were that the intensity and the total number of CT states increased, as the number of H2 O molecules in the cluster increased. The proliferation of CT states with cluster size implies that the CT states form a band of delocalized hole states in bulk water. It is expected that as the conditions of bulk water are approached, this CT band will resemble the experimentally observed absorption peak associated with the OH charge-transfer band in water. Continuing work on OH aims to confirm these hypotheses, and to further investigate the dynamics of the excited CT state. FIG. 9. Plots of transition oscillator strength versus transition wavelength for (a) OH and OH-1W dimers; (b) OH-2W clusters; (c) OH-3W clusters; and (d) OH-4W clusters.
red-shifted due to polarization of the solvent water. While the lowest energy CT states involve H2 O molecules that are nearest neighbors to the OH, we observe that some of the donor MOs involved have contributions from more than one H2 O molecule, and are hence delocalized. The MOs associated with higher energy CT transitions generally display even greater delocalization as linear combinations of oxygen p orbitals on the various water molecules in the complexes are involved. Analyzing the clusters containing three and four water molecules shows that delocalization of the CT states is spread beyond the first hydration shell of OH; however, these CT states generally lie 1 eV or more above the low ones. Still, even taking only the low-lying CT states into account, the CT absorption of hydrated OH may be due to a band of delocalized hole states in liquid water. There have been recent efforts to understand delocalized hole states in liquid water,28, 29, 32, 33 and further progress may help in the understanding of CT dynamics of hydrated OH.
ACKNOWLEDGMENTS
G.J.H. wishes to thank Edinboro University of Pennsylvania for granting a 6 month sabbatical leave. L.V.S. acknowledges support from the National Science Foundation (Grant No. CHE-0955419). 1 W.
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